Solve y=5x-7/2x-6

$$y = \frac { 5 x - 7 } { 2 x - 6 }$$

Solve for x

$$x=-\frac{7-6y}{2y-5}$$

$$y\neq \frac{5}{2}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-3\right).

$$y\times 2\left(x-3\right)=5x-7$$

Use the distributive property to multiply y\times 2 by x-3.

$$2yx-3y\times 2=5x-7$$

Multiply -3 and 2 to get -6.

$$2yx-6y=5x-7$$

Subtract 5x from both sides.

$$2yx-6y-5x=-7$$

Add 6y to both sides.

$$2yx-5x=-7+6y$$

Combine all terms containing x.

$$\left(2y-5\right)x=-7+6y$$

The equation is in standard form.

$$\left(2y-5\right)x=6y-7$$

Divide both sides by 2y-5.

$$\frac{\left(2y-5\right)x}{2y-5}=\frac{6y-7}{2y-5}$$

Dividing by 2y-5 undoes the multiplication by 2y-5.

$$x=\frac{6y-7}{2y-5}$$

Variable x cannot be equal to 3.

$$x=\frac{6y-7}{2y-5}\text{, }x\neq 3$$

Solve for y

$$y=-\frac{7-5x}{2\left(x-3\right)}$$

$$x\neq 3$$